SUPPLEMENTARY INFORMATION

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1 DETECTION LIMITS IN PHOTOTHERMAL MICROSCOPY Alexander Gaiduk, Paul V. Ruijgrok, Mustafa Yorulmaz, Michel Orrit Institute of Physics, Leiden University, P.O. Box 9504, 300 RA Leiden, The Netherlands SUPPLEMENTARY INFORMATION Contents: A: Thermal and optical constants for selected materials. Photothermal strength for different media.. B: Calculated absorption cross-sections for gold nanoparticles of 0 nm and 5 nm in diameter for different wavelengths in media with various refractive indices... 3 C: Analysis of the variations of SNR... 4 D: Noise of the photothermal detection... 6 E: Comparison of the Cat s eye and 50/50 BS configurations... 7 F: AFM measurements of 0 nm gold on glass surface... 8 G: Analysis of the PMMA layer thickness... 9 H: Analysis of the number of dye molecules in fluorospheres... 10

2 A: Thermal and optical constants for selected materials. Photothermal strength for different media Table A1: Thermal and optical constants for selected materials at room temperature and normal pressure. 1 Σ = PT FOM = n n media n C p κ n 1 n 1 r T [Jm -3 K -1 ] [Wm -1 K -1 n ] n [K -1 ] T C p T κ [m 3 J -1 ] [m W -1 ] BK7 glass PMMA Water Glycerol Ethanol Hexane Decane Pentane Chloroform Carbon tetrachloride Carbon disulfide BK 7 = nbk 7 + n Values are from: (a) Bialkowski, S.E., Photothermal Spectroscopy Methods for Chemical Analysis, Wiley, (b) CRC Handbook of Chemistry and Physics n n 1 n T C p T carbon disulfide carbon tetrachloride chloroform hexane decane ethanol glycerol water temperature [ C] Figure A1: Photothermal strength (Σ PT ) for various media. The temperature dependence (as defined by the refractive index behavior with temperature) is shown for water, ethanol and carbon disulfide. Alexander Gaiduk, Paul V. Ruijgrok, Mustafa Yorulmaz, Michel Orrit

3 B: Calculated absorption cross-sections for gold nanoparticles of 0 nm and 5 nm in diameter for different wavelengths in media with various refractive indices Figure B1: Absorption cross-sections for gold nanoparticles 0 nm and 5 nm in diameter calculated for media with different refractive indices and various wavelengths. Calculations are based on Mie theory [C.F. Bohren, D.R.Huffman Absorption and Scattering of Light by Small Particles Wiley, 1998] and use the dielectric functions of Johnson and Christy [P.B.Johnson, R.W.Christy, Optical Constants of Noble Metals Phys.Rev.B 6 (1) (197)] Table B1: Calculated σ abs (in nm²) for 0 nm diameter gold nanoparticles for selected wavelengths and media. refractive index (n) λ (nm) 1.63 (carbon disulfide) 1.47 (glycerol) 1.37 (hexane) 1.33 (water) Alexander Gaiduk, Paul V. Ruijgrok, Mustafa Yorulmaz, Michel Orrit 3

4 C: Analysis of the variations of SNR As follows from Eq.4 in the main text, SNR is equal to: 1 n 1 σ P abs probe t SNR n Pheat πω λ Ω T C A hν 0. probe probe p (C1) where ω 0.probe is the focal radius (beam waist) of the probe beam λ probe is the wavelength of the probe light Ω is the modulation frequency n is the refractive index of the medium n/ T is the variation of the refractive index of the medium with temperature C p is the specific heat capacity of the medium A is the area of the heating beam in the focal plane (= πω 0.heat ) P heat is the heating power P probe is the probe power hν is the energy of the probe photon (= hc/λ probe ) t is the integration time of photothermal detection Let us consider the equation for the characteristic length of heat diffusion (r th ): Dth κ rth = = Ω C Ω, (C) p where D th is the thermal diffusivity coefficient, κ is the thermal conductivity of the medium. Substituting Eq. C into C1, we obtain: 1 r th n 1 σ P abs probe t 1 r P th σ abs probe t SNR n Pheat = FOM Pdiss πω 0. probe λ probe T κ A hν πω 0. probe λ probe A hν (C3), where FOM n 1 = n is defined as a figure of merit of photothermal media. T κ Eq. C3 expresses the SNR as a function of (i) a combination of thermal and optical parameters of the r media λ parameters. th probe n 1 n at a given probe wavelength; and (ii) heat and probe power dependent T κ Alexander Gaiduk, Paul V. Ruijgrok, Mustafa Yorulmaz, Michel Orrit 4

5 r th In practice, the proportionality parameter in the SNR equation,, is kept close to 1 by λ probe choosing the modulation frequency of the heat beam such that r th matches the probe beam waist. Efficient scattering of the probe beam would be achieved in this case. Alexander Gaiduk, Paul V. Ruijgrok, Mustafa Yorulmaz, Michel Orrit 5

6 D: Noise of the photothermal detection The total noise σ total in the optical experiments, contributed by the detector noise σ detector, the photon noise σ shot and the laser noise σ laser is defined as follows: ( ) σ = σ + σ + σ = σ + Fσ + σ = σ + F BPhν + n P (D1) total detector shot laser detector photon laser detector laser where σ detector is the detector noise, provided by manufacturer, independent of detected power F is excess noise factor, resulting from the excess noise generated by the photodiode B is the measurements bandwidth P is the measured power hν is the energy of the detected photons n laser is the proportionality coefficient describing the laser noise dependent on the laser power The noise measured for the Ti:sapphire laser (Mira, Coherent, pumped with Coherent Verdi V10) and the photodetector at different gains is depicted in Fig. D1. There is no contribution of the noise that scales linearly with the laser power within the range of powers we measured, from 1 µw to 1.8 mw. That suggests a photon-noise limited detection of the photothermal signal. Noise (nw) photon noise 180 µw (gain4) 1.8 mw (gain3) max. detector power 18 µw (gain5) E power measured at PD (mw) Figure D1. Noise power as a function of the optical power measured at the photodetector (PD). Horizontal dotted lines indicate the detector noise at a given sensitivity (detector gain). These lines also indicate the maximum detector power at a given sensitivity as specified by the manufacturer: 180 nw for the gain 10 7 A/V (not pictured), 1.8 µw for the gain 10 6 A/V (not pictured), 18 µw for the gain 10 5 A/V, 180 µw for the gain 10 4 A/V, 1.8 mw for the gain 10 3 A/V and 18 mw for the gain 10 A/V (not pictured). The sensitivity of the Si-PIN detector is specified to be 0.5 A/W in the nm range. The dashed line represents the calculated photon noise, which scales with the square root of the measured probe power. The results of the noise measurements (for detector gains A/V) are pictured with full dots. Solid lines show results of the fit to the equation below with σ detector = 0.49 nw, n laser = 0, F = 3.3 (for 10 3 A/V gain); σ detector = nw, n laser = 0, F =.9 (for 10 4 A/V gain); σ detector = 0.03 nw, n laser = 0, F = (for 10 5 A/V gain). Alexander Gaiduk, Paul V. Ruijgrok, Mustafa Yorulmaz, Michel Orrit 6

7 E: Comparison of the Cat s eye and 50/50 BS configurations Figure E1. Schematic representation of experimental setup Cat s eye (left) and 50/50 BS (right) configurations and indications of the probe power. Considering only the effect of probe laser on the photothermal SNR for two different reflector configurations we note: 1. For the cat s eye configuration S ~rp 0, and N ~ rp 0, there r is the reflection coefficient specific to the refraction index contrast at the glass/sample interface. Thus for the cat s eye configuration SNR = rp 0.. For the 50/50 BS configuration S ~ rp 0, and N ~ rp, thus SNR = rp 0 The SNR should be twice better in the cat's eye configuration, but is experimentally found to be similar to that in the 50/50 BS configuration. Alexander Gaiduk, Paul V. Ruijgrok, Mustafa Yorulmaz, Michel Orrit 7

8 F: AFM measurements of 0 nm gold on glass surface # 5 5 µm particles height (nm) Figure F1. (left) AFM topography image of 0 nm gold particles on glass surface. (right) Histogram of height distributions of these particles (64 particles in total). Mean height is 14±1.5 nm Z (nm) µm (µm) Figure F. (left) AFM topography image of 0 nm gold particles on glass surface (zoom in to the area of the image presented in G1). (right) A cross section along the line indicated in the image shows the height for three particles. 0.1 µm Figure F3. SEM image of 0 nm gold particles Alexander Gaiduk, Paul V. Ruijgrok, Mustafa Yorulmaz, Michel Orrit 8

9 G: Analysis of the PMMA layer thickness 50 µm Figure G1: (Right): AFM topography image of a scratch on the PMMA film. The PMMA layer is prepared by spin coating 50 µl of 30 g/l PMMA solution in toluene. (Left): A cross section at the position indicated in AFM image. The height of the PMMA layer is about 100 nm. Alexander Gaiduk, Paul V. Ruijgrok, Mustafa Yorulmaz, Michel Orrit 9

10 H: Analysis of the number of dye molecules in fluorospheres # molecules per bead diameter of beads [µm] Figure H1: Number of dye molecules per fluorescent bead of various diameters as suggested by Invitrogen manual FluoSpheres Fluorescent Microspheres [ for yellow-green beads (fluorescein doping). In our experiment, we used Nile Red beads, which have a different number of dyes per bead Abs wavelength (nm) Figure H: Absorption spectrum of Nile red beads in water solution measured with a SHIMADZU Spectrophotometer UV170 PharmaSpec. On average, assuming all the dye molecules are embedded in the beads, the number of dye molecules per fluorescent bead estimated from the extinction coefficient would be about 30. However, free dye molecules present in solution may contribute to the absorption spectrum and would reduce the actual number of dyes per single bead. The molar extinction coefficient ε = M -1 cm -1 at nm. [ and M. M. Davis and H. B. Hetzer, "Titrimetric and equilibrium studies using indicators related to Nile Blue A," Anal. Chem., 38, , 1966] Calculations of the number of dye molecules per single bead: 1. 0 nm Nile Red beads are wt% in the stock solution. Volume of a bead is L and there are с bead.stock = beads/l. stock solution is diluted in water with 1:100 ratio, resulting in c 0 = с bead.stock /100 = beads/l 3. the extinction of the sample with c 0 beads concentration is = εcl (see Fig.H). ε = M -1 cm -1, L=0. cm. 4. Estimate of dye molecule concentration: c = M/L, thus of molecules n = c N A = molecules/l 5. thus the number of dye molecules per bead is N = n/c 0 = 7-39 molecules/bead Alexander Gaiduk, Paul V. Ruijgrok, Mustafa Yorulmaz, Michel Orrit 10

11 (a) (b) Fluorescence (f) (d) (e) (c) 1 kcounts/10ms (g) (h) (k) (i) time (s) Figure H3: Examples of fluorescence bleaching time traces taken on several 0 nm beads. Traces show single step photobleaching and blinking events, indicating that only few dye molecules are embedded in each bead. Assuming the count rate per single molecule of 100 counts/10 ms (from a single-step photobleaching event with the smallest signal difference with dark counts), a single bead would contain N=000/100=0 fluorescent dyes. This number corresponds well to the number of dyes estimated from the absorption measurements (Fig.H), but disagrees with the number provided by the manufacturer for another dye (Fig.H1). Excitation power in the experiment: P heat = 4.5 µw. Alexander Gaiduk, Paul V. Ruijgrok, Mustafa Yorulmaz, Michel Orrit 11